3.5.10 Operations of Fixed Point Types

Static Semantics

1

The following attributes
are defined for every fixed point subtype S:

2/1

S'Small

{8652/0005}
{AI95-00054-01}
S'Small denotes the small of the type of S. The value of this
attribute is of the type universal_real. {specifiable
(of Small for fixed point types) [partial]}{Small
clause}Small may be specified for nonderived ordinary fixed point types via an attribute_definition_clause
(see 13.3); the expression of such a clause
shall be static.

3

S'Delta

S'Delta denotes the delta
of the fixed point subtype S. The value of this attribute is of the type
universal_real.

3.a

Reason: The delta is associated
with the subtype as opposed to the type, because of the possibility
of an (obsolescent) delta_constraint.

4

S'Fore

S'Fore yields the minimum number
of characters needed before the decimal point for the decimal representation
of any value of the subtype S, assuming that the representation does
not include an exponent, but includes a one-character prefix that is
either a minus sign or a space. (This minimum number does not include
superfluous zeros or underlines, and is at least 2.) The value of this
attribute is of the type universal_integer.

5

S'Aft

S'Aft yields the number of decimal
digits needed after the decimal point to accommodate the delta
of the subtype S, unless the delta of the subtype S is greater
than 0.1, in which case the attribute yields the value one. [(S'Aft is
the smallest positive integer N for which (10**N)*S'Delta is greater
than or equal to one.)] The value of this attribute is of the type universal_integer.

6

The following additional
attributes are defined for every decimal fixed point subtype S:

7

S'Digits

S'Digits denotes the digits
of the decimal fixed point subtype S, which corresponds to the number
of decimal digits that are representable in objects of the subtype. The
value of this attribute is of the type universal_integer. Its
value is determined as follows: {digits
(of a decimal fixed point subtype)}

Implementation Note: Although a decimal
subtype can be both range-constrained and digits-constrained, the digits
constraint is intended to control the Size attribute of the subtype.
For decimal types, Size can be important because input/output of decimal
types is so common.

10

The digits of a base subtype
is the largest integer D such that the range –(10**D–1)*delta
.. +(10**D–1)*delta is included in the base range
of the type.

11

S'Scale

S'Scale denotes the scale
of the subtype S, defined as the value N such that S'Delta = 10.0**(–N).
{scale (of a decimal fixed point subtype)}[The scale indicates the position of the point relative
to the rightmost significant digits of values of subtype S.] The value
of this attribute is of the type universal_integer.

11.a

Ramification: S'Scale is negative if
S'Delta is greater than one. By contrast, S'Aft is always positive.

12

S'Round

S'Round denotes a function with
the following specification:

13

function S'Round(X : universal_real)return S'Base

14

The function returns the value obtained by
rounding X (away from 0, if X is midway between two values of the type
of S).

NOTES

15

39 All subtypes of a fixed point type will
have the same value for the Delta attribute, in the absence of delta_constraints
(see J.3).

16

40 S'Scale is not always the same as S'Aft
for a decimal subtype; for example, if S'Delta = 1.0 then S'Aft is 1
while S'Scale is 0.

17

41 {predefined
operations (of a fixed point type) [partial]}The
predefined operations of a fixed point type include the assignment operation,
qualification, the membership tests, and explicit conversion to and from
other numeric types. They also include the relational operators and the
following predefined arithmetic operators: the binary and unary adding
operators – and +, multiplying operators, and the unary operator
abs.

18

42 As for all types, objects of a fixed
point type have Size and Address attributes (see 13.3).
Other attributes of fixed point types are defined in A.5.4.

Wording Changes from Ada 95

18.a/2

{8652/0005}
{AI95-00054-01}
Corrigendum: Clarified that small
may be specified only for ordinary fixed point types.